Newton-Based Optimization for Kullback-Leibler Nonnegative Tensor Factorizations

Abstract

Tensor factorizations with nonnegative constraints have found application in analyzing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g., count data), which leads to sparse tensors that can be modeled by sparse factor matrices. In this paper we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback-Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton and quasi-Newton methods. We compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.

Clarified notation in section 3.1.1, and used simpler score() function in section B.2

References in corpus (1)

• On Tensors, Sparsity, and Nonnegative Factorizations

Cited by in corpus (5)

• Generalized Canonical Polyadic Tensor Decomposition
• Stochastic Gradients for Large-Scale Tensor Decomposition
• A generalizable framework for low-rank tensor completion with numerical priors
• Taming numerical imprecision by adapting the KL divergence to negative probabilities
• A quadratically convergent proximal algorithm for nonnegative tensor decomposition